NAME
    acrd - inverse trigonometric chord of a unit circle

SYNOPSIS
    acrd(x [,eps])

TYPES
    x		number (real or complex)
    eps		0 < real < 1, defaults to epsilon()

    return	number

DESCRIPTION
    Calculate angle of unit circle chord of length x to a multiple of eps with error less in
    absolute value than .75 * eps.

    A chord of a circle is a straight line segment whose endpoints lie on a arc of a circle.
    A chord extended infinitely on both directions into a line would produce a secant line.

    This function is sometimes called chord, is equivalent to:

	acrd(x) = 2 * asin(x / 2)

EXAMPLE
    ; print acrd(1/2), acrd(5/7), acrd(42/7)
    0.50536051028415730696 0.73041444258073348124 3.14159265358979323846-3.52549434807817210092i

    ; print acrd(1, 1e-5), acrd(1, 1e-10), acrd(1, 1e-15), acrd(1, 1e-20)
    1.0472 1.0471975512 1.047197551196598 1.04719755119659774616

    ; print acrd(2 + 3i, 1e-5), acrd(2 + 3i, 1e-10)
    1.0472+2.63392i 1.0471975512+2.6339157938i

    ; pi = pi(1e-20)
    ; print acrd(pi/6), acrd(pi/2), acrd(pi)
    0.52977229404847186194 1.80667822153302569472 3.14159265358979323846-2.04645495709510115864i

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qacrd(NUMBER *x, NUMBER *eps)
    COMPLEX *c_acrd(COMPLEX *x, NUMBER *eps)

SEE ALSO
    sin, cos, tan, cot, sec, csc
    asin, acos, atan, acot, asec, acsc
    coversin, vercos, covercos
    aversin, acoversin, avercos, acovercos
    haversin, hacoversin, havercos, hacovercos
    ahaversin, hacoversin, havercos, ahacovercos
    exsec, aexsec, excsc, aexcsc
    crd
    cas, cis
    epsilon

EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
	https://en.wikipedia.org/wiki/Versine
	https://en.wikipedia.org/wiki/Exsecant
	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
	https://en.wikipedia.org/wiki/Chord_(geometry)
	https://en.wikipedia.org/wiki/Secant_line
	https://en.wikipedia.org/wiki/Hartley_transform#cas
	https://en.wikipedia.org/wiki/Cis_(mathematics)

## Copyright (C) 2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
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## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
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## Under source code control:	2023/10/02 16:49:42
## File existed as early as:	2023
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